Question

Find the ratio between the area of the shaded and the unshaded portions of the following figure $:$

• A. $11:3$
• B. $1:3$
• C. $10:3$
• D. $14:3$

Answer 1

The correct option is A $11:3$

Let the radius of the circle be $r$
Therefore,
Length of rectangle=$3r$
Breadth of rectangle=$2r$
Area of circle and semicircle(shaded region)=$\pi r^2+\frac{\pi r^2}{2}$
=$\frac{3}{2}\pi r^2$
=$\frac{3\times 22}{2\times 7}{r}^2$
=$\frac{33}{7}{r}^2$
Area of rectangle=$\left(3r{)}^2\right(2r)$
=$6r^2$
Area of unshaded region=$(6r^2-\frac{3}{2}\pi r^2)$
=$(6-\frac{3\times 22}{2\times 7})r^2$
=$(6-\frac{33}{7})r^2$
=$\left(\frac{42-33}{7}\right)r^2$
=$\left(\frac{9}{7}\right)r^2$
Ratio of shaded region and the unshaded region=$\frac{33}{7}{r}^2:\left(\right(\frac{9}{7}\left)r^2\right)$
=$11:3$